Cole and Asher collected some beads. If Cole gave Asher 56 beads, both would have an equal number of beads. If Asher gave Cole 42 beads, Cole would have 5 times as many beads as Asher. Find the number of beads each of them had.
- Cole?
- Asher?
| Case 1 |
Case 2 |
| Cole |
Asher |
Cole |
Asher |
| 3 u + 56 |
3 u - 56 |
5 u - 42 |
1 u + 42 |
| - 56 |
+ 56 |
+ 42 |
- 42 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of beads the same. LCM of 2 and 6 is 6.
The number of beads that Asher had at first is the same in both cases.
3 u - 56 = 1 u + 42
3 u - 1 u = 56 + 42
2 u = 98
1 u = 98 ÷ 2 = 49
Number of beads that Cole had
= 3 u + 56
= 3 x 49 + 56
= 203
(b)
Number of beads that Asher had
= 3 u - 56
= 3 x 49 - 56
= 91
Answer(s): (a) 203; (b) 91
